A current drawback of spintronics is the large power that is usually required for magnetic writing, in contrast with nanoelectronics, which relies on "zero-current," gate-controlled operations. Efforts have been made to control the spin-relaxation rate, the Curie temperature, or the magnetic anisotropy with a gate voltage, but these effects are usually small and volatile. We used ferroelectric tunnel junctions with ferromagnetic electrodes to demonstrate local, large, and nonvolatile control of carrier spin polarization by electrically switching ferroelectric polarization. Our results represent a giant type of interfacial magnetoelectric coupling and suggest a low-power approach for spin-based information control.